Transesterification is used for the manufacture of fatty acid esters, for example, by using oils and fats which are esters of fatty acids and glycerin. Alkali catalysts such as caustic soda, zinc catalysts, and lipase can be used as catalysts. Furthermore, it was also suggested to conduct the reaction in a supercritical state, without the addition of a catalyst (Japanese Patent Publication Nos. 9-235573A, 7-197047A, and 2000-143586A).